A study of quasi-Gorenstein rings II: Deformation of quasi-Gorenstein property

Shimomoto, Kazuma; Taniguchi, Naoki; Tavanfar, Ehsan

doi:10.1016/j.jalgebra.2020.06.032

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Some Preliminary Background1

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2022

2023

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Cited by 2 publications

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“…(i) The "quasi-Gorenstein deformation" condition in Theorem 3.2 may not be replaced by an arbitrary deformation in general. Firstly, the quasi-Gorenstein property does not deform in general by [ShTaTa20]. Therefore, an arbitrary deformation of a quasi-Gorenstein Buchsbaum ring as in Theorem 3.2 is not necessarily quasi-Gorenstein.…”

Section: Some Preliminary Backgroundmentioning

confidence: 99%

Remarks on the Small Cohen-Macaulay conjecture and new instances of maximal Cohen-Macaulay modules

Shimomoto¹,

Tavanfar²

2022

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We show that any quasi-Gorenstein deformation of a 3-dimensional quasi-Gorenstein Buchsbaum local ring with I-invariant 1 admits a maximal Cohen-Macaulay module, provided it is a quotient of a Gorenstein ring. Such a class of rings includes two instances of unique factorization domains constructed by Marcel-Schenzel and by Imtiaz-Schenzel, respectively. Apart from this result, motivated by the small Cohen-Macaulay conjecture in prime characteristic, we examine a question about when the Frobenius pushforward F e * (M ) of an R-module M comprises a maximal Cohen-Macaulay direct summand in both local and graded cases.

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Section: Some Preliminary Backgroundmentioning

confidence: 99%